An approximation method to circular arcs

DOI10.1016/j.amc.2012.07.038zbMath1288.65020OpenAlexW2077595533MaRDI QIDQ2449254

Zhi Liu, Li Zhang, Jie-qing Tan, Xiao-yan Chen

Publication date: 7 May 2014

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2012.07.038

zbMATH Keywords

circular arcapproximation orderHausdorff distancequartic Bézier curvecontrol pointgraphical examplecurvature continuous spline approximation algorithm

Mathematics Subject Classification ID

Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (14)

Some new \(G^1\) quartic parametric approximants of circular arcs ⋮ Curvature approximation of circular arcs by low-degree parametric polynomials ⋮ Circular arc approximation using polygons ⋮ Optimal parameter values for approximating conic sections by the quartic Bézier curves ⋮ Interpolation of circular arcs by parametric polynomials of maximal geometric smoothness ⋮ \(G^1\) approximation of conic sections by quartic Bézier curves ⋮ Approximation of conic section by quartic Bézier curve with endpoints continuity condition ⋮ Circular arc approximation by hexic polynomial curves ⋮ Circular sector area preserving approximation of circular arcs by geometrically smooth parametric polynomials ⋮ Unnamed Item ⋮ Circle approximation by \(G^2\) Bézier curves of degree \(n\) with \(2 n - 1\) extreme points ⋮ A new method approximating offset curve by Bézier curve using parallel derivative curves ⋮ A general framework for the optimal approximation of circular arcs by parametric polynomial curves ⋮ The \(G^2\) and \(C^2\) rational quadratic trigonometric Bézier curve with two shape parameters with applications

Cites Work

• Bézier representation of the constrained dual Bernstein polynomials
• A note on iterative process for \(G^{2}\)-multi degree reduction of Bézier curves
• On polynomial approximation of circular arcs and helices
• An approximation of circular arcs by quartic Bézier curves
• The best \(G^{1}\) cubic and \(G^{2}\) quartic Bézier approximations of circular arcs
• High-order approximation of conic sections by quadratic splines
• Good approximation of circles by curvature-continuous Bézier curves
• Approximation of circular arcs by cubic polynomials
• Circular arc approximation by quintic polynomial curves
• Approximation of circular arcs by Bézier curves
• An \(O(h^{2n})\) Hermite approximation for conic sections
• Unnamed Item

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